Answer:
Step-by-step explanation:
Find common denominators. 10 is the common denominator. Multiply 2 to numerator and denominator of -3/5
(-3/5)(2/2) = -6/10
x + 1/10 = -6/10
Isolate the x. Subtract 1/10 from both sides
x + 1/10 (-1/10) = -6/10 (-1/10)
x = -6/10 - 1/10
x = -7/10
-7/10 is your answer for x
hope this helps
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
-15
Step-by-step explanation:
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